#### Stokes force

###### Equation

The resistance is defined in terms of the fluid viscosity and the sphere's velocity as follows:

$ F_v = b v $ |

Stokes explicitly calculated the resistance experienced by the sphere and determined that viscosity is proportional to the sphere's radius and its velocity, leading to the following equation for resistance:

$ F_v =6 \pi \eta r v $ |

ID:(4871, 0)

#### Particle velocity in electric field

###### Equation

A charged particle

$ F = q E $ |

This force is opposed by a force due to the effect of the medium that can be modeled by Stokes law

$ F_v =6 \pi \eta r v $ |

If both forces are equalized, it is obtained that the particle moves with a constant speed equal to

$ \vec{v} = \mu \vec{E} $ |

with mobility equal to

$ \mu =\displaystyle\frac{ q }{6 \pi \eta a }$ |

ID:(11997, 0)

#### Particle mobility in electric field

###### Equation

To equalize the force caused by the electric field

$ F = q E $ |

with the opposing force that is modeled with Stokes law

$ F_v =6 \pi \eta r v $ |

the relationship is obtained

$ \vec{v} = \mu \vec{E} $ |

with mobility equal to

$ \mu =\displaystyle\frac{ q }{6 \pi \eta a }$ |

ID:(11998, 0)